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For handling missing data, newer methods such as those based on multiple imputation are generally more accurate than older ones and entail weaker assumptions. Yet most do assume that data are missing at random (MAR). The issue of assessing whether the MAR assumption holds to begin with has been largely ignored. In fact, no way to directly test MAR is available. We propose an alternate assumption, MAR+, that can be tested. MAR+ always implies MAR, so inability to reject MAR+ bodes well for MAR. In contrast, MAR implies MAR+ not universally, but under certain conditions that are often plausible; thus, rejection of MAR+ can raise suspicions about MAR. Our approach is applicable mainly to studies that are not longitudinal. We present five illustrative medical examples, in most of which it turns out that MAR+ fails. There are limits to the ability of sophisticated statistical methods to correct for missing data. Efforts to try to prevent missing data in the first place should therefore receive more attention in medical studies than they have heretofore attracted. If MAR+ is found to fail for a study whose data have already been gathered, extra caution may need to be exercised in the interpretation of the results.

The Johnson-NeJ~~n technique is a statistical tool used most frequently in educational and psychological applications. This paper starts by briefly reviewing the Johnson-Neyman technique and suggesting when it should and should not be used; then several different modifications and extensions of the Johnson-Neyman technique, all of them conceptually simple are proposed. The close relation between confidence intervals and regions of significance of the .Johnson-Neyman t~'lle is pointed out. The problem of what to do when more than two groups are being compared is considered. The situation of more than one criterion variable is also considered.

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